Is it possible to set selected new users to require clearance on their first posts

I've a relatively new forum and occasionally when a new user joins I'm suspicious of their username and email address. Some of them blow their cover right away, occasionally they turn out to be okay and a few never seem to post. Is there any functionality to mark someone as suspicious so that when they post it requires admin approval before it hits the board?

You should be able to do this with permissions and a secondary UserGroup.

Create a secondary group. Set UserGroup permission "Follow message moderation rules" to "Never". Call the group "Untrusted" or somesuch.
As required, add users to this group (AdminCP)
(If I understand that "Follow message moderation rules" permission correctly) Such users will have all their posts put in the Mod Q for release.
As required, remove users from the secondary group if/when they are trusted.

I interpreted this case as
- the default position is posts are not Moderated. This is not the result of a promotion. All members get this, normally.
- exceptionally, some users require to be Moderated; demoted temporarily if you like.

Since there isn't a "revoke" option on User Group permissions, that leaves only Never. Hence my suggestion.

The only way I can see to NOT use Never is to have the default user (Registered) as "Moderated" but promote them all immediately by default to a secondary group where "Follow Moderation Rules" is set to Allow.
And then DEMOTE (remove secondary group) those who are being watched. And PROMOTE them again when the watch is lifted.
Without going into it further, I'm not sure how you'd create a setup whereby members were instantly promoted (added to a 2ndry group) on registration, BUT not ever automatically added back to it if they were manually removed/demoted.